Solve sqrt{2*35000/9.71}

$$\sqrt{ \frac{ 2 \cdot 35000 }{ 9.71 } }$$

Evaluate

$$\frac{1000\sqrt{6797}}{971}\approx 84.906200138$$

Solution Steps

Multiply 2 and 35000 to get 70000.

$$\sqrt{\frac{70000}{9.71}}$$

Expand \frac{70000}{9.71} by multiplying both numerator and the denominator by 100.

$$\sqrt{\frac{7000000}{971}}$$

Rewrite the square root of the division \sqrt{\frac{7000000}{971}} as the division of square roots \frac{\sqrt{7000000}}{\sqrt{971}}.

$$\frac{\sqrt{7000000}}{\sqrt{971}}$$

Factor 7000000=1000^{2}\times 7. Rewrite the square root of the product \sqrt{1000^{2}\times 7} as the product of square roots \sqrt{1000^{2}}\sqrt{7}. Take the square root of 1000^{2}.

$$\frac{1000\sqrt{7}}{\sqrt{971}}$$

Rationalize the denominator of \frac{1000\sqrt{7}}{\sqrt{971}} by multiplying numerator and denominator by \sqrt{971}.

$$\frac{1000\sqrt{7}\sqrt{971}}{\left(\sqrt{971}\right)^{2}}$$

The square of \sqrt{971} is 971.

$$\frac{1000\sqrt{7}\sqrt{971}}{971}$$

To multiply \sqrt{7} and \sqrt{971}, multiply the numbers under the square root.

$$\frac{1000\sqrt{6797}}{971}$$